PRP Records

Probable Primes Top 10000

(290751 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
97513^181378-2^(181378-1)86540Robert Price01/2016
975224588^3305+3305^2458886530Hans Havermann08/2020
975383^45080-286513Lelio R Paula08/2013
9754(2^287367+2570)/286506Stefano Morozzi01/2020
9756(78557*2^287351+1)/61186504Lelio R Paula06/2014
9755(2^287360+1006)/286504Stefano Morozzi01/2020
975725*29^59147+2093686498Curtis Bright05/2015
97582^287298+187135986486Enzo Doria05/2016
9759118^41740-11786481Norbert Schneider08/2018
97603*10^86478+8986479Robert Price03/2017
97612^287272-7904986478Paul Bourdelais02/2012
9762(2^287259+2846)/286474Stefano Morozzi01/2020
9763906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
9764811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
9765779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
9766768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
9767700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
9768652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
9769377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
9770255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
9771187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
9772(10^86453-1)/986453Lew Baxter10/2000
9773(2^287172+658)/286448Stefano Morozzi01/2020
9774(2^287146+2542)/286440Stefano Morozzi01/2020
9775(2^287136+1726)/286437Stefano Morozzi01/2020
9776(2^287128+958)/286434Stefano Morozzi01/2020
977787^44563-86^4456386431Robert Price05/2015
9778(26*10^86424-41)/386425Robert Price02/2022
97796^111057+6186420Lelio R Paula12/2015
97802^287057-10990986413Enzo Doria04/2014
97815^123608+2286399Lelio R Paula10/2015
978210832^21411-21411^1083286388Norbert Schneider01/2022
9783(2^286970+618)/286387Stefano Morozzi01/2020
9784(2^286916+2646)/286371Stefano Morozzi01/2020
9785(2^286907+3690)/286368Stefano Morozzi01/2020
9786(31*10^86364-121)/986365Robert Price06/2016
9787(2^286868+2686)/286356Stefano Morozzi01/2020
97882^286859+7166386354Enzo Doria04/2016
9789(2^286845+1866)/286349Stefano Morozzi01/2020
97902^286740+2983586318Lelio R Paula10/2013
97912*10^86310+9^8631086311Mike Oakes05/2011
979211^82878-186086309Enzo Doria12/2012
97932223^25780+25780^222386285Norbert Schneider12/2019
97942^286547+1609586260Lelio R Paula10/2013
9795(58*10^86242+329)/986243Robert Price11/2017
97962^286455-11042786232Enzo Doria05/2014
9797(37*10^86230+53)/986231Robert Price05/2015
97988*3^180700+586217Lelio R Paula08/2014
97993^180697-4086215Lelio R Paula12/2015
9800(2^286383+3386)/286210Stefano Morozzi01/2020
9801(13*2^286318-1)/1325786188Lelio R Paula02/2014
9802(2^286295+1934)/286184Stefano Morozzi01/2020
9803(157*10^86179-1)/386181Robert Price01/2022
9804(2^286251+3974)/286170Stefano Morozzi01/2020
98052^286165+7786145Lelio R Paula08/2012
98069*2^286140+786138Lelio R Paula08/2014
9807(2^286128+1762)/286133Stefano Morozzi01/2020
9808(118*10^86131+71)/986133Robert Price11/2021
9809(29*2^286108-1)/200236786123Lelio R Paula02/2014
9810(2^286077+1122)/286118Stefano Morozzi01/2020
981110^86110+16111386111Patrick De Geest07/2013
981210^86110-6986110Robert Price05/2011
98132^286036-86968810586106Lelio R Paula07/2016
9814(2^285946+2358)/286079Stefano Morozzi01/2020
98155*10^86076-2186077Robert Price12/2021
9817(77*10^86072+31)/986073Robert Price10/2015
9816(2^285926+3382)/286073Stefano Morozzi01/2020
98182^285923+34586072Lelio R Paula09/2013
981913^77266-9086070Lelio R Paula11/2015
98202^285910-45890386068Enzo Doria04/2015
98212^285904-12586066Lelio R Paula08/2012
9822(2^285882+2830)/286059Stefano Morozzi01/2020
98232^285836+6583586046Lelio R Paula09/2013
982421587^9670+9670^2158786034Hans Havermann08/2020
9825(2^285766+78557)/386024Lelio R Paula01/2013
9826(2^285732+2682)/286014Stefano Morozzi01/2020
9827(5*10^86011-107)/386012Robert Price01/2017
98286^110522+16386003Lelio R Paula12/2015
982941^53323-40^5332385999Robert Price07/2012
98302^285678-10961785998Enzo Doria04/2014
98316^110506-1667385991Enzo Doria02/2013
98322^285619-300193585980Paul Bourdelais04/2022
98332^285569-74185965Lelio R Paula09/2013
9834(32*10^85964+31)/985965Robert Price05/2015
9835133^40466+13285944Norbert Schneider02/2019
983623378^4743+4743^2337885939Hans Havermann08/2020
98376*10^85910-785911Dmitry Domanov11/2010
9838(412*10^85897-7)/985899Robert Price10/2017
98394*10^85881+6385882Robert Price06/2016
9840(2^285257+1514)/285871Stefano Morozzi01/2020
9841(2^285248+3738)/285868Stefano Morozzi01/2020
9842(10^85864+53)/985864Robert Price01/2015
98432^285230+34585863Lelio R Paula09/2013
984421774^8777+8777^2177485863Hans Havermann08/2020
9845(5*10^85855-473)/985855Robert Price12/2017
98462^285199+7568385854Enzo Doria04/2016
9847(76*10^85847-211)/985848Robert Price10/2017
9848p(17832)#/2+51285845Robert Price05/2017
9849(16*10^85839+167)/385840Robert Price10/2017
985011^82426-123085838Enzo Doria11/2012
9851(14727^20593-1)/1472685830Serge Batalov08/2020
98522^285113-10988185828Enzo Doria04/2014
9853(2^285033+1670)/285804Stefano Morozzi01/2020
9854(2^285033+3854)/285804Stefano Morozzi01/2020
9855(2^285035+3194)/285804Stefano Morozzi01/2020
98565^122746-9285796Lelio R Paula10/2015
98572^285001-11346185794Enzo Doria08/2014
9858(11*10^85782-131)/385783Robert Price02/2017
9859(2^284963+2778)/285783Stefano Morozzi01/2020
9860(2^284960+3570)/285782Stefano Morozzi01/2020
9861(2^284937+1706)/285775Stefano Morozzi01/2020
98632^284913-11049185768Enzo Doria05/2014
98626^110220+4785768Lelio R Paula12/2015
9864(1966^26041-1)/196585765Serge Batalov08/2020
986520698^13909+13909^2069885758Hans Havermann07/2020
98663*6^110202-585755Lelio R Paula10/2014
98679*10^85746+3785747Robert Price12/2020
9868(157^39047-1)/15685742Alexander Zhirkov06/2016
9869(3^179705+7)/25085739Lelio R Paula12/2012
9870(9127^21649-1)/912685734Serge Batalov08/2020
98712^284734-655585714Lelio R Paula09/2013
9872(10^85712+53)/985712Robert Price01/2015
98733*10^85703+1185704Robert Price11/2017
9874(6883*2^284668-1)/385697Lelio R Paula04/2015
987520728^13621+13621^2072885694Hans Havermann07/2020
987622126^7459+7459^2212685687Hans Havermann07/2020
9877(9311^21589-1)/931085683Serge Batalov08/2020
987820^65855+8385680Lelio R Paula01/2016
98796^110105+5385679Lelio R Paula12/2015
98803*10^85672-7385673Robert Price02/2021
9881(10^85666-97)/385666Robert Kinser10/2017
98832^284567-760585664Lelio R Paula09/2013
98829*5^122555-285664Lelio R Paula10/2014
98845^122554-1485662Lelio R Paula10/2015
98859*5^122543+485655Lelio R Paula10/2014
9886(7*10^85647+173)/985647Robert Price01/2022
98883^179489-2^(179489-1)85639Robert Price01/2016
9887(2^284487+1970)/285639Stefano Morozzi01/2020
9889(2^284477+1614)/285636Stefano Morozzi01/2020
989023693^4114+4114^2369385633Hans Havermann07/2020
989119690^19941+19941^1969085632Norbert Schneider03/2020
98922^284429+17785622Lelio R Paula08/2012
98932*3^179452+585621Lelio R Paula07/2014
989421036^11711+11711^2103685587Hans Havermann07/2020
9896(19^66919+3^66919)/2285572Robert Price07/2013
9895(2^284265+602)/285572Stefano Morozzi01/2020
989766^47023-6585561Norbert Schneider11/2014
9898(2^284226+3802)/285561Stefano Morozzi01/2020
9899(2^284228+2170)/285561Stefano Morozzi01/2020
9900(56*10^85554+169)/985555Robert Price03/2022
99016^109943+1385553Lelio R Paula12/2015
99022^284183-474785548Yves Minet05/2019
9903(5637^22807-1)/563685547Serge Batalov08/2020
990420782^13071+13071^2078285546Hans Havermann08/2020
9905(2^284167-509203)/3456477585536Lelio R Paula01/2013
9906(2^284136+2262)/285534Stefano Morozzi01/2020
99072^284133-385533M. Frind & P. Underwood07/2002
99082^284113+31585527Lelio R Paula09/2013
9909(2^284098+3082)/285522Stefano Morozzi01/2020
9910(29*10^85517-23)/385518Robert Price03/2022
9911(2^284070+1482)/285514Stefano Morozzi01/2020
9912(2^284068+2866)/285513Stefano Morozzi01/2020
9913(8721^21701-1)/872085511Serge Batalov08/2020
991422085^7438+7438^2208585502Hans Havermann07/2020
9915(28*10^85500+149)/385501Robert Price10/2017
9916(16*10^85495-19)/385496Robert Price03/2016
99172^284004+17785494Lelio R Paula08/2012
9918(16*10^85473-91)/385474Robert Price06/2016
991966*10^85468+785470Robert Price07/2020
99203^179120+2285462Robert Price12/2013
99212^283872-279224985454Enzo Doria03/2016
9922(4703^23269-1)/470285449Serge Batalov08/2020
9923(29*10^85438+259)/985439Robert Price04/2017
99242^283817+8287585438Lelio R Paula09/2013
9925(2^283815-5)/20185435Lelio R Paula01/2013
99262^283796-12585432Lelio R Paula08/2012
9927(10174^21319-1)/1017385432Serge Batalov08/2020
9928(29*2^283784-1)/1385428Lelio R Paula02/2014
992915^72592-2885375Lelio R Paula11/2015
99302^283604-5869585374Lelio R Paula09/2013
993121863^8034+8034^2186385374Hans Havermann08/2020
9933(44*10^85370-503)/985371Robert Price10/2017
9932(2^283597+1854)/285371Stefano Morozzi01/2020
9934496^31671+31671^49685369Norbert Schneider07/2017
9935(2^283578+478)/285366Stefano Morozzi01/2020
9936(15*2^283583-1)/10305185364Lelio R Paula02/2014
993715^72572+9285352Lelio R Paula11/2015
99386*10^85350-7985351Robert Price03/2022
99392^283473-161585334Lelio R Paula09/2013
9940(2^283469+2934)/285333Stefano Morozzi01/2020
99412^283466-1585332Lelio R Paula08/2012
9942(2^283437+3446)/285323Stefano Morozzi01/2020
994319966^18761+18761^1996685320Hans Havermann07/2020
9944(2^283411+3894)/285315Stefano Morozzi01/2020
994511^81916-702085307Enzo Doria02/2013
99466^109626-785306Lelio R Paula11/2014
99472^283374-11032785305Enzo Doria05/2014
994833*10^85297+785299Robert Price07/2016
9949(6010^22573-1)/600985297Serge Batalov08/2020
99501137^27908+27908^113785281Norbert Schneider04/2020
995118^67933+4185275Lelio R Paula11/2015
99522^283271-10934185274Enzo Doria04/2014
9953(2^283266+3678)/285272Stefano Morozzi01/2020
995419688^19855-19855^1968885262Norbert Schneider03/2020
9955(2^283216+1926)/285257Stefano Morozzi01/2020
9956(5*10^85254-191)/385255Robert Price05/2021
9957(25*10^85249-73)/385250Robert Price09/2016
99582*5^121959+385246Lelio R Paula10/2014
995919834^19834+894785235Henri Lifchitz11/2004
99602^283140+191585234Lelio R Paula09/2013
99613*10^85227-9785228Robert Price08/2017
9962(16*10^85221-31)/385222Robert Price03/2016
9963(2^283096+3186)/285221Stefano Morozzi01/2020
99642^283083+186938385217Enzo Doria05/2016
9965(24737*2^283051+1)/1785211Lelio R Paula06/2014
9966(2^283032+78557)/385201Lelio R Paula01/2013
99672^283026-10989385200Enzo Doria04/2014
9968(2^283012+78557)/12985193Lelio R Paula01/2013
9969(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
99702^282860-10972785150Enzo Doria04/2014
9971(2^282847+13)/385145Stefano Morozzi03/2020
9972(35*10^85141-611)/985142Robert Price02/2022
99732^282819+186941385138Enzo Doria05/2016
99743^178428+285132Ray Chandler07/2011
997519985^18162+18162^1998585120Hans Havermann07/2020
9976(22699*2^282742+1)/7385117Lelio R Paula06/2014
9977(16^70687+5^70687)/2185115Robert Price07/2013
9978(2^282732+738)/285111Stefano Morozzi01/2020
9979(2^282720+1590)/285107Stefano Morozzi01/2020
9980(3^178352-2)/785095Lelio R Paula12/2012
998122150^6939+6939^2215085085Hans Havermann07/2020
998211^81699-279085081Enzo Doria12/2012
99832^282612-9585075Lelio R Paula08/2012
99842^282609-406985074Yves Minet02/2018
998575^45366-285065Lelio R Paula08/2013
9986(2^282550+1918)/285056Stefano Morozzi01/2020
9987(2^282515+3786)/285046Stefano Morozzi01/2020
99882^282511+6985045Lelio R Paula08/2012
998969^46249+285045Lelio R Paula06/2013
9990(2^282488+2382)/285038Stefano Morozzi01/2020
9991(2^282489+1862)/285038Stefano Morozzi01/2020
99923^178226+1085036Robert Price10/2013
9993(2^282475+1050)/285034Stefano Morozzi01/2020
9994(182*10^85017+43)/985019Robert Price11/2017
9995(14*10^85010+73)/385011Robert Price04/2016
99969*2^282338-784994Lelio R Paula08/2014
9997(9913*2^282330-1)/157800384988Lelio R Paula04/2015
99985*10^84985-3184986Robert Price12/2021
999920025^17504+17504^2002584969Hans Havermann07/2020
100002^282203+584952Lelio R Paula08/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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